J. Aust. Math. Soc.  74 (2003), 101-109
Biseparating linear maps between continuous vector-valued function spaces

 Hwa-Long Gau   Department of Mathematics   National Central University   Chung-Li   Taiwan 320   R.O.C.  hlgau@math.ncu.edu.tw
 Jyh-Shyang Jeang   Department of Applied Mathematics   National Sun Yat-sen University   Kaohsiung   Taiwan 804   R.O.C.  jeangjs@math.nsysu.edu.tw
 and
 Ngai-Ching Wong   Department of Applied Mathematics   National Sun Yat-sen University   Kaohsiung   Taiwan 804   R.O.C.  wong@math.nsysu.edu.tw

Abstract
Let X, Y be compact Hausdorff spaces and E, F be Banach spaces. A linear map is separating if T f, T g have disjoint cozeroes whenever f, g have disjoint cozeroes. We prove that a biseparating linear bijection T (that is, T and are separating) is a weighted composition operator . Here, h is a function from Y into the set of invertible linear operators from E onto F, and is a homeomorphism from Y onto X. We also show that T is bounded if and only if  h(y)  is a bounded operator from E onto F for all y in Y. In this case, h is continuous with respect to the strong operator topology.